plumiEquations of lines: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 6.1 Equations of lines, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
Questions from
Paper
All papers
Exam
All years
Loading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDF
All 15 questions on Equations of lines, as a list
- June 2025, Pure Core 1, Q7 (8 marks): A 3-D coordinate system, whose units are metres, is set up to model a street containing telephone cables T1 and T2. The cables are modelled as straight lines wi
- June 2025, AS Pure Core, Q6 (7 marks): K O K O K O K O 6 The equations of two lines, l1 and l2, are l r 1 27 OO and l r 10 10 OO. = - KK OO + m KK - = KK OO + n KK 1 | 2 | 3 19 10 10 - - L P L P L P
- June 2024, Pure Core 1, Q11 (7 marks): A 3-D coordinate system, whose units are metres, is set up to model a construction site. The construction site contains four vertical poles P1, P2, P3 and P4. T
- June 2024, AS Pure Core, Q5 (10 marks): The line through points A 8 ( , 7 , 2 ) and B 11 ( , 9 0 , ) is denoted by L1. - - - (a) Find a vector equation for L1. [2] (b) Determine whether the point ( 26
- June 2023, AS Pure Core, Q2 (8 marks): The lines L1 and L2 have the following equations. J N J N 5 5 - K O K O L : r 6 2 = + - KK OO m KK OO 1 15 2 - L P L P J N J N 24 3 K O K O L : r 1 1 = + KK OO
- June 2022, Pure Core 2, Q1 (6 marks): (a) Find a vector which is perpendicular to both 3i - 5j - k and i + 3j - 4k. [1] The equations of two lines are r = 2i + 3j + 3k+ m(i - 2j + k) and r = i + 11j
- June 2022, AS Pure Core, Q1 (8 marks): K O K O 1 (a) Determine whether the point (19, -12, 17) lies on the line r 2 2 OO. [3] = - KK OO + m KK - 7 4 L P L P J N J N 1 3 - K O K O Vectors a and b are
- November 2021, Pure Core 1, Q4 (11 marks): Points A, B and C have coordinates (4, 2, 0), (1, 5, 3) and (1, 4, -2) respectively. The line l passes through A and B. (a) Find a cartesian equation for l. [3]
- November 2021, Pure Core 2, Q3 (9 marks): K O K O 3 The line l1 has equation r 3 2 OO. = - KK OO + m KK 3 2 - L P L P J N 2 K O The plane P has equation r. 5 4 . KK - OO = 3 - L P (a) Find the position
- November 2021, AS Pure Core, Q1 (5 marks): The lines l1 and l2 have the following equations. J N J N 8 2 - K O K O l r 11 5 | = - + KK OO m KK OO 1 2 3 - L P L P J N J N 6 3 - - K O K O l r 11 1 | = + KK
- November 2021, AS Pure Core, Q9 (13 marks): The points P(3, 5, 21 ) and Q( 1 - , 3, 16 ) are on the ceiling of a long straight underground tunnel. - - A ventilation shaft must be dug from the point M on t
- November 2020, Pure Core 2, Q4 (9 marks): The equations of two intersecting lines l1 and l2 are J N J N J N J N 1 2 7 1 - K O K O K O K O l : r 0 1 l : r 9 1 = KK OO + m KK OO = KK OO + n KK OO 1 2 a 3
- November 2020, AS Pure Core, Q7 (6 marks): The equations of two intersecting lines are J N J N J N J N 12 2 2 3 - - K O K O K O K O r = a 2 OO r = 0 1 + + KK OO m KK KK OO n KK OO 1 1 5 1 - - L P L P L P
- June 2019, AS Pure Core, Q3 (10 marks): The position vector of point A is a 9 i 2 j 6 k . =- + + The line l passes through A and is perpendicular to a. (a) Determine the shortest distance between the
- June 2018, AS Pure Core, Q1 (5 marks): f p and f p. 1 (i) Find a vector which is perpendicular to both [2] 3 6 - 2 4 - (ii) The cartesian equation of a line is x y z 3 2 + . 4 = - = 2 [3] Express the
Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? OCR A-Level Further Maths past papers.
The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.